Determining profile parameters of a structure formed on a semiconductor wafer using a dispersion function relating process parameter to dispersion

ABSTRACT

An optical metrology model is created for a structure formed on a semiconductor wafer. The optical metrology model comprises one or more profile parameters, one or more process parameters, and dispersion. A dispersion function is obtained that relates the dispersion to at least one of the one or more process parameters. A simulated diffraction signal is generated using the optical metrology model and a value for the at least one of the process parameters and a value for the dispersion. The value for the dispersion is calculated using the value for the at least one of the process parameter and the dispersion function. A measured diffraction signal of the structure is obtained. The measured diffraction signal is compared to the simulated diffraction signal. One or more profile parameters of the structure and one or more process parameters are determined based on the comparison of the measured diffraction signal to the simulated diffraction signal.

BACKGROUND

1. Field

The present application generally relates to optical metrology of astructure formed on a semiconductor wafer, and, more particularly, togenerating a simulated diffraction signal using a dispersion functionrelating process parameter to dispersion.

2. Related Art

Optical metrology involves directing an incident beam at a structure,measuring the resulting diffracted beam, and analyzing the diffractedbeam to determine one or more profile parameters of the structure. Insemiconductor manufacturing, optical metrology is typically used forquality assurance. For example, after the fabrication of a structure ona semiconductor wafer, an optical metrology tool is used to determinethe profile of the structure. By determination of the profile of thestructure, the quality of the fabrication process utilized to form thestructure can be evaluated.

In one conventional optical metrology process, a measured diffractionsignal is compared to simulated diffraction signals. The simulateddiffraction signals are generated using an optical metrology model. Theoptical metrology model includes a number of parameters that are variedin generating the simulated diffraction signals. Increasing the numberof parameters of the optical metrology model can increase the accuracyof the optical metrology process when those parameters are notcorrelated to each other. However, parameters are typically correlatedto each other to some degree. Thus, increasing the number of parametersof the optical metrology model that are varied can also increase theinstability of the model.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is an architectural diagram illustrating an exemplary fabricationtool and an exemplary optical metrology tool;

FIG. 2 depicts the exemplary optical metrology tool in more detail;

FIG. 3 is a flowchart of an exemplary process of examining a structureformed on a semiconductor wafer;

FIG. 4 depicts an exemplary structure characterized using a set ofprofile parameters;

FIG. 5A is a flowchart of an exemplary process of defining a dispersionfunction relating a process parameter to a dispersion;

FIG. 5B is a flowchart of an exemplary process of defining a dispersionfunction relating a process parameter to a dispersion using a processsimulator;

FIG. 6 is a flowchart of an exemplary process of controlling thefabrication tool;

FIG. 7 is an exemplary flowchart for automated process control using alibrary;

FIG. 8 is an exemplary flowchart for automated process control using atrained machine learning system; and

FIG. 9 is an exemplary block diagram of a system for determining andutilizing profile parameters and process parameters for automatedprocess and equipment control.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENT(S)

In order to provide a more thorough understanding of the presentinvention, the following description sets forth numerous specificdetails, such as specific configurations, parameters, examples, and thelike. It should be recognized, however, that such description is notintended as a limitation on the scope of the present invention, but isintended to provide a better understanding of the exemplary embodiments.

In order to facilitate description of the present invention, asemiconductor wafer may be utilized to illustrate an application of theconcept. The methods and processes equally apply to other work piecesthat have a structure.

FIG. 1 depicts one or more wafers 102 processed in an exemplaryfabrication tool 104. One or more semiconductor fabrication processescan be performed on one or more wafers 102 in fabrication tool 104.Typically a number of wafers 102 are processed as a batch, commonlyreferred to as a wafer lot, in fabrication tool 104. For example, awafer lot of 25 wafers 102 can be processed as a batch in fabricationtool 104. It should be recognized, however, that the number of wafers102 in a wafer lot can vary.

One or more process parameters are used in performing the one or moresemiconductor fabrication processes. For example, the one or moreprocess parameters can include deposition conditions, annealingconditions, etching conditions, temperature, gas pressure, vaporizationspeed, and the like. The etching conditions can include surface propertychanges, etching residual components, and the like.

Typically, the one or more process parameters are set to define arecipe. Also, the same recipe (i.e., a setting of the one or moreprocess parameters) is used to process the wafers in one wafer lot. Oneor more individual process parameters of a particular recipe can beadjusted while processing the wafers in one wafer lot. The one or moreprocess parameters can also be set to different values to definedifferent recipes. Different recipes can be used to process differentwafer lots. Thus, one recipe can be used to process one wafer lot, andanother recipe can be used to process another wafer lot.

Fabrication tool 104 can be various types of fabrication tools, such asa coater/developer tool, plasma etch tool, cleaning tool, chemical vapordeposition (CVD) tool, and the like, that perform various fabricationprocesses. For example, when fabrication tool 104 is a coater/developertool, the fabrication process includes depositing/developing aphotoresist layer on one or more wafers 102. The one or more processparameters can include temperature. Thus, in this example, variations intemperatures used to perform the deposition/development process canresult in a variation in the photoresist layer, such as the thickness ofthe photoresist layer, deposited/developed using the coater/developertool.

As depicted in FIG. 1, after one or more semiconductor fabricationprocesses are performed on one or more wafers 102 in fabrication tool104, one or more wafers 102 can be examined using optical metrology tool106. As will be described in more detail below, optical metrology tool106 can be used to determine one or more profile parameters of astructure formed on one or more wafers 102.

As depicted in FIG. 2, optical metrology tool 106 can include aphotometric device with a source 204 and a detector 206. The photometricdevice can be a reflectometer, ellipsometer, hybridreflectometer/ellipsometer, and the like.

A structure 202 formed on wafer 102 is illuminated by an incident beamfrom source 204. Diffracted beams are received by detector 206. Detector206 converts the diffracted beam into a measured diffraction signal,which can include reflectance, tan (Ψ), cos (Δ), Fourier coefficients,and the like. Although a zero-order diffraction signal is depicted inFIG. 2, it should be recognized that non-zero orders can also be used.

Optical metrology tool 106 also includes a processing module 208configured to receive the measured diffraction signal and analyze themeasured diffraction signal. Processing module 208 can include aprocessor 210 and a computer-readable medium 212. It should berecognized, however, that processing module 208 can include any numberof components in various configurations.

In one exemplary embodiment, processing module 208 is configured todetermine one or more profile parameters of structure 202 using anynumber of methods which provide a best matching diffraction signal tothe measured diffraction signal. These methods can include alibrary-based process, or a regression based process using simulateddiffraction signals obtained by rigorous coupled wave analysis andmachine learning systems. See, U.S. Pat. No. 6,943,900, titledGENERATION OF A LIBRARY OF PERIODIC GRATING DIFFRACTION SIGNALS, filedon Jul. 16, 2001, issued Sep. 13, 2005, which is incorporated herein byreference in its entirety; U.S. Pat. No. 6,785,638, titled METHOD ANDSYSTEM OF DYNAMIC LEARNING THROUGH A REGRESSION-BASED LIBRARY GENERATIONPROCESS, filed on Aug. 6, 2001, issued Aug. 31, 2004, which isincorporated herein by reference in its entirety; U.S. Pat. No.6,891,626, titled CACHING OF INTRA-LAYER CALCULATIONS FOR RAPID RIGOROUSCOUPLED-WAVE ANALYSES, filed on Jan. 25, 2001, issued May 10, 2005,which is incorporated herein by reference in its entirety; and abandonedU.S. patent application Ser. No. 10/608,300, titled OPTICAL METROLOGY OFSTRUCTURES FORMED ON SEMICONDUCTOR WAFERS USING MACHINE LEARNINGSYSTEMS, filed on Jun. 27, 2003, which is incorporated herein byreference in its entirety.

With reference to FIG. 3, an exemplary process 300 is depicted ofexamining a structure formed on a semiconductor wafer using an opticalmetrology model. It should be recognized that exemplary process 300 canbe performed prior or subsequent to the structure actually being formedon the semiconductor wafer.

In step 302, an optical metrology model is obtained. The opticalmetrology model has one or more profile parameters, one or more processparameters, and a dispersion. A dispersion function is defined to relatethe process parameter to the dispersion. The dispersion function can beexpressed in various forms, such as wavelength by wavelength tabletform, the optical property of each wavelength can be a function ofprocess parameters, or using dispersion models with model parametersvaried with the process parameters. It should be recognized, however,that the optical metrology model can also include any number ofadditional parameters.

The profile parameters of an optical metrology model characterize thegeometric characteristics of a structure. For example, FIG. 4 depicts anexemplary structure characterized using a set of profile parameters. Inparticular, the bottom width of the first layer of the structure ischaracterized using profile parameter w1. The top width of the firstlayer and the bottom width of the second width of the structure arecharacterized using profile parameter w2. The top width of the secondlayer of the structure is characterized using profile parameter w3. Theheight of the first layer of the structure is characterized usingprofile parameter h1. The height of the second layer of the structure ischaracterized using profile parameter h2. It should be recognized thatthe structure can have various shapes and can be characterized using anynumber of profile parameters.

As described above, the process parameters of an optical metrology modelcharacterize one or more process conditions of a process for fabricatinga structure. For example, with reference to FIG. 1, the processparameter can characterize a process condition in fabrication tool 104used to fabricate a structure on wafer 102. Examples of processparameters include deposition conditions (such as temperature, gaspressure, vaporization speed, etc.), annealing conditions, etchingconditions (surface property change, etching residual components, etc.),and the like.

The dispersion characterizes optical properties of a material of thestructure, the structure being formed by the process. For example, thedispersion can include the refractive indices (n) and the extinctioncoefficients (k) of a material. The optical metrology model can includeseparate dispersions for each material of the structure. For example,with reference again to FIG. 4, a first dispersion (n_(s) & k_(s)) cancorrespond to the material of the substrate on which the structure isformed, such as silicon. A second dispersion (n₁ & k₁) can correspond tothe material of the first layer of the structure, such as oxide. A thirddispersion (n₂ & k₂) can correspond to the material of the second layerof the structure, such as poly-silicon.

With reference again to FIG. 3, in step 304, a dispersion function isobtained that relates the dispersion to at least one of the processparameters. For example, with reference to FIG. 4, the dispersionfunction can relate the dispersion corresponding to the material of thesecond layer of the structure (n₂ & k₂) to the temperature used infabricating the structure in fabrication tool 104 (FIG. 1). An exemplaryprocess of developing the dispersion function will be described in moredetail below.

With reference again to FIG. 3, in step 306, a simulated diffractionsignal is generated using the optical metrology model and a value forthe at least one process parameter that is related to the dispersion bythe dispersion function obtained in step 304 and a value for thedispersion. The value of the dispersion is calculated using the valuefor the at least one process parameter and the dispersion function. Byrelating the process parameter to the dispersion, the number of varyingparameters in the optical metrology model is reduced with the desiredaccuracy, which increases the stability of the model.

For example, with reference again to FIG. 4, assume that the dispersionfunction obtained in step 304 (FIG. 3) related the dispersioncorresponding to the material of the second layer of the structure (n₂ &k₂) to the temperature used in fabricating the structure in fabricationtool 104 (FIG. 1). Assume that in generating a simulated diffractionsignal, a value for the temperature is specified (T1). Thus, the valueof n₂ & k₂ is calculated using the dispersion function obtained in step304 (FIG. 3) and T1.

As described in more detail below, the values of the remainingdispersions (n_(s) & k_(s), n₁ & k₁) can be fixed to set values orfloated, meaning that the values can be varied when additional simulateddiffraction signals are generated. A set of values is specified for theprofile parameters. The simulated diffraction signal is then generatedusing the values for the profile parameters, the process parameters, andthe dispersions. In particular, the simulated diffraction signal can begenerated by applying Maxwell's equations and using a numerical analysistechnique to solve Maxwell's equations, such as Rigorous Coupled WaveAnalysis (RCWA). See, U.S. patent application Ser. No. 09/770,997,titled CACHING OF INTRA-LAYER CALCULATIONS FOR RAPID RIGOROUSCOUPLED-WAVE ANALYSES, filed on Jan. 25, 2001, now U.S. Pat. No.6,891,626, which is incorporated herein by reference in its entirety.The simulated diffraction signal can be generated using a machinelearning system (MLS) employing a machine learning algorithm, such asback-propagation, radial basis function, support vector, kernelregression, and the like. See abandoned U.S. patent application Ser. No.10/608,300, titled OPTICAL METROLOGY OF STRUCTURES FORMED ONSEMICONDUCTOR WAFERS USING MACHINE LEARNING SYSTEMS, filed on Jun. 27,2003, which is incorporated herein by reference in its entirety.

With reference again to FIG. 3, in step 308, a measured diffractionsignal measured off the structure is obtained. For example, as describedabove, with reference to FIG. 1, after the structure is formed usingfabrication tool 104, optical metrology tool 106 can be used to measurea diffraction signal off the structure formed on the wafer.

With reference again to FIG. 3, in step 310, the measured diffractionsignal is compared to the simulated diffraction signal generated in step306. In step 312, one or more profile parameters of the structure aredetermined based on the comparison of the measured diffraction signal tothe simulated diffraction signal.

In particular, if the measured diffraction signal and the simulateddiffraction signal match within one or more matching criteria such asgoodness of fit and/or cost function, then the profile parameters usedto generate the matching simulated diffraction signal are assumed tocharacterize the geometric shape of the structure. The dispersion usedto generate the matching simulated diffraction signal is assumed tocharacterize the optical properties of the one or more materials of thestructure to which the dispersion corresponds. The process parametersused to generate optical properties of the one or more materials andthen generate the matching simulated diffraction signal are assumed tocharacterize the process conditions used to fabricate the structure.

If the measured diffraction signal and the simulated diffraction signaldo not match within one or more matching criteria such as goodness offit and/or cost function, then the measured diffraction signal iscompared to one or more additional simulated diffraction signals until amatch is found. The additional simulated diffraction signals aregenerated using a value of at least one profile parameter, processparameter, or dispersion that is different than the simulateddiffraction signal that did not match the measured diffraction signal.

Values of one or more of the profile parameters (e.g., w1, w2, w3, h1,h2 of FIG. 4) can be changed in generating the additional simulateddiffraction signals. Values of one or more of the process parameters canbe changed in generating the additional simulated diffraction signals.If the values of the process parameters that are related to thedispersions in the dispersion function obtained in step 304 are changed,then the values of the dispersions are recalculated using the values ofthe process parameter and the dispersion function obtained in step 304.The values of the dispersions that are not related to process parametersin the dispersion function obtained in step 304 are fixed to set valuesor are allowed to float, meaning they are changed in generating theadditional simulated diffraction signals.

For example, assume that the dispersion function obtained in step 304related temperature to the dispersion corresponding to the material ofthe second layer of the structure (n₂ & k₂) depicted in FIG. 4. Assumethat a first value of the temperature (T1) was used in generating thefirst simulated diffraction signal. As described above, a first value ofn₂ & k₂ was calculated using the dispersion function obtained in step304 and the first value of T1. Assume now that a second value of thetemperature (T2) is used in generating an additional simulateddiffraction signal (i.e., a second simulated diffraction signal). Thus,in the present example, a second value of n₂ & k₂ is calculated usingthe dispersion function obtained in step 304 and T2.

As described above, the remaining dispersions, which are not related toprocess parameters, can be fixed to set values or floated. For example,values of n_(s) & k_(s), which correspond to the material of thesubstrate on which the structure in FIG. 4 is formed, can be fixed toset values in generating the additional simulated diffraction signals.Values of n₁ & k₁, which corresponds to the material of the first layerof the structure in FIG. 4, can be floated (varied) in generating theadditional simulated diffraction signals independent of the changes tothe values for the process parameters.

In a library-based process, the additional simulated diffractionssignals are generated in advance and stored in a library. In aregression-based process, the additional simulated diffraction signal isnot generated until after the measured diffraction signal is found notto match the simulated diffraction signal to which it was compared.

With reference to FIG. 5A, an exemplary process 500 is depicted ofdeveloping the dispersion function relating a process parameter to adispersion. It should be recognized that exemplary process 500 can beperformed in advance of exemplary process 300 (FIG. 3). It should alsobe recognized that exemplary process 500 can be performed in advance orsubsequent to forming the structure to be examined.

In step 502, a first wafer is fabricated using a first value of theprocess parameter to be correlated to a dispersion. For example, assumethe process parameter is temperature. Also assume that the dispersion isn₂ & k₂, which corresponds to the second layer of the structure depictedin FIG. 4. Thus, with reference to FIG. 1, the first wafer is fabricatedusing a first value of temperature in fabrication tool 104. Inparticular, the second layer of the structure depicted in FIG. 4 isformed using the first value of temperature in fabrication tool 104.

With reference again to FIG. 5A, in step 504, a first value of thedispersion is measured from the fabricated first wafer. Returning to theexample above, the value of the n & k of the second layer of thestructure depicted in FIG. 4 is measured.

In step 506, a second wafer is fabricated using a second value of theprocess parameter. In step 508, a second value of the dispersion ismeasured from the fabricated second wafer.

In step 510, a third wafer is fabricated using a third value of theprocess parameter. In step 512, a third value of the dispersion ismeasured from the fabricated third wafer.

The first, second, and third values for the process parameter used insteps 502, 506, and 510 are different from each other. In one exemplaryembodiment, all other process parameters are kept constant infabricating the first, second, and third wafers.

For example, assume again that the process parameter is temperature.Thus, in this example, with reference to FIG. 1, the first, second, andthird wafers are fabricated in fabrication tool 104 using a first,second, and third temperature settings (T1, T2, and T3) that aredifferent. All other process parameters, such as pressure, vaporizationspeed, and the like, are kept constant in fabricating the first, second,and third wafers in fabrication tool 104.

In one exemplary embodiment, the first, second, and third values of thedispersion can be measured using optical metrology tool 106. Inparticular, assume test structures with the shape shown in FIG. 4 arefabricated on the first, second, and third wafers using fabrication tool104 (FIG. 1). Measured diffraction signals are measured off the teststructures using optical metrology tool 106 (FIG. 1). The measureddiffraction signals are compared to simulated diffraction signals todetermine the first, second, and third values of the dispersions (e.g.,n & k) of the second layers of the test structures on the first, second,and third wafers. Note, the simulated diffraction signals used indetermining the first, second, and third values of n & k of the secondlayers of the test structures are generated by floating the values of n& k. It is understood that more than three sets of wafers can befabricated with different values of the one or more process parametersin order to provide a bigger data sample for fitting the dispersionfunction.

In step 514, the dispersion function is defined using the first, second,and third values of the dispersion and the first, second, and thirdvalues of the process parameter. For example, a second-order polynomialcan be fitted to the first, second, and third values of the dispersionand the first, second, and third values of the process parameter. In oneexemplary embodiment, the dispersion function is defined for variouswavelengths λ. Stated more generally, the second-order polynomial can befitted to any number of dispersions (n & k) and process parameters (p)with coefficients: an₀(λ), an₁(λ), an₂(λ), ak₀(λ), ak₁(λ), and ak₂(λ) byminimizing the following error functions:

$\begin{matrix}{{{Enr}(\lambda)} = {\sum\limits_{j = 1}^{k}\left( {{{an}_{0}(\lambda)} + {{{an}_{1}(\lambda)} \cdot p_{j}} + {{{an}_{2}(\lambda)} \cdot p_{j}^{2}} - {n_{j}(\lambda)}} \right)^{2}}} & (1.1) \\{{{Ekr}(\lambda)} = {\sum\limits_{j = 1}^{k}\left( {{{ak}_{0}(\lambda)} + {{{ak}_{1}(\lambda)} \cdot p_{j}} + {{{ak}_{2}(\lambda)} \cdot p_{j}^{2}} - {k_{j}(\lambda)}} \right)^{2}}} & (1.2)\end{matrix}$This fitting can be performed wavelength by wavelength. The number ofsamples (test structures) is larger than the number of the polynomialorder plus one. It should be recognized that various functions can befitted, such as a Taylor series in multi-dimensions.

Although a linear relationship of the variables is used in the examplesabove, it should be recognized that non-linear functional relationshipsbetween the variables can be used, such as arbitrary functions,composite functions, and the like. Least squares fit solutions to apolynomial may include the determinant, matrix, independent parametersolutions, and the like. Least squares fit to an arbitrary function mayinclude nonlinear fitting methods, searching parameter space methods,grid search methods, gradient search methods, expansion methods, theMarquardt method, and the like. For a more detailed discussion of thesetechniques, see Bevington, et al., “Data Reduction and Error Analysisfor the Physical Sciences,” Third Edition, pages 116-177, which isincorporated herein by reference.

As described above, in step 306, a simulated diffraction signal usingthe optical metrology model is generated with the value of thedispersion being calculated using the value for the process parameterand the dispersion function. Continuing with the foregoing example, thevalue of n & k can be calculated for process parameter (p) at awavelength as follows:n(λ)=an ₀(λ)+an ₁(λ)·p+an ₂(λ)·p ²  (2.1)k(λ)=ak ₀(λ)+ak ₁(λ)·p+ak ₂(λ)·p ²  (2.2)

The simulated diffraction signal is best matched with a measureddiffraction signal. The profile parameters and process parameters thatare used to generate the simulated diffraction signal that best matchesthe measured diffraction signal are assumed to characterize one or moreprofile parameters of the structure from which the measured diffractionsignal was measured and the process parameters used to fabricate thestructure.

The profile parameters and process parameters can be used to evaluatethe fabrication tool and/or fabrication process used to fabricate thestructure. For example, the profile parameters can be used to evaluatethe fabrication tool used in the fabrication process. The processparameters can be used to monitor the process condition of thefabrication process performed using the fabrication tool. Thus,fabrication tool and/or fabrication process can be controlled to achievea more stable performance and increase yield.

With reference to FIG. 5B, an exemplary process 550 is depicted ofdeveloping the dispersion function relating one or more processparameters to a dispersion using process simulation. As mentioned above,it should be recognized that exemplary process 550 can be performed inadvance of exemplary process 300 (FIG. 3). In step 552, one or moreprocess parameters of the fabrication process are selected. As mentionedabove, the one or more process parameters can include depositionconditions, annealing conditions, etching conditions, temperature, gaspressure, vaporization speed, and the like. The etching conditions caninclude surface property changes, etching residual components, and thelike. If the fabrication process is a deposition, the temperature of thechamber and/or the gas pressure may be selected as the processparameters. In step 554, a set of values of the one or more processparameters is determined based on empirical data or experience with theapplication or recipe. The one or more process parameters selected arethe process parameter that will be correlated to the dispersion.

In step 556, fabrication of the wafer structure is simulated using aprocess simulator for each set of values of the selected one or moreprocess parameters determined in step 554. Simulation of a fabricationprocess is typically done with process simulators such as Athena™ fromSilvaco International, Prolith™ from KLA-Tencor, Solid-C from Sigma-CGmbh, TCAD™ from Synopsis, and the like. Specifics of the recipe and thewafer structure and process parameters are provided to the processsimulator. One of the typical output of the process simulation is thestructure profile after the simulated process is completed. For example,assume the process parameter of interest is temperature. Also assumethat the dispersion is n₂ & k₂, which corresponds to the second layer ofthe structure depicted in FIG. 4. Thus, simulation of fabrication of thewafer structure is simulated using a value of temperature. Inparticular, simulation of formation of the second layer of the structuredepicted in FIG. 4 is done using the first value of temperature utilizedby the process simulator.

With reference again to FIG. 5B, in step 558, a value of the dispersionis determined for the simulated wafer structure for each value of theone or more process parameters selected in step 552. Returning to theexample above, the value of the n & k of the second layer of thestructure depicted in FIG. 4 may be obtained by setting up n & k as anoutput of the process simulator or may be calculated using n & ksimulation software. Examples of n & k simulation software include n & kAnalyzer™ from n&k Technology, Prolith™ from KLA-Tencor, and the like.In one exemplary embodiment, all other process parameters are keptconstant in the process simulation runs needed for step 558. Forexample, assume again that the process parameter is temperature. Thus,in this example, all other process parameters used in the processsimulator, such as pressure, vaporization speed, and the like, are keptconstant.

In step 560, the dispersion function is defined using the values of thedispersion and the values of the selected one or more processparameters. For example, if only one process parameter is selected, asecond-order polynomial can be fitted to the values of the dispersionand the values of the process parameter. In one exemplary embodiment,the dispersion function is defined for various wavelengths λ. Asdescribed above, the second-order polynomial can be fitted to any numberof dispersions (n & k) and process parameters (p) with coefficients:an₀(λ), an₁(λ), an₂(λ), ak₀(λ), ak₁(λ), and ak₂(λ) by minimizing thefollowing error functions expressed in equation (1.1) and (1.2) above.This fitting can be performed wavelength by wavelength. The number ofsamples (test structures) is larger than the number of the polynomialorder plus one. It should be recognized that various functions can befitted, such as a Taylor series in multi-dimensions.

As mentioned above, a linear relationship of the variables is used inthe examples above, it should be recognized that non-linear functionalrelationships between the variables can be used, such as arbitraryfunctions, composite functions, and the like. Least squares fitsolutions to a polynomial may include the determinant, matrix,independent parameter solutions, and the like. Least squares fit to anarbitrary function may include nonlinear fitting methods, searchingparameter space methods, grid search methods, gradient search methods,expansion methods, the Marquardt method, and the like. For a moredetailed discussion of these techniques, see Bevington, et al., “DataReduction and Error Analysis for the Physical Sciences,” Third Edition,pages 116-177, which is incorporated herein by reference.

As described above, in step 306 of FIG. 3, a simulated diffractionsignal using the optical metrology model is generated with the value ofthe dispersion being calculated using the value for the one or moreprocess parameters and the dispersion function. Continuing with theforegoing example, the value of n & k can be calculated for processparameter (p) at a wavelength as depicted in equations (2.1) and (2.2).The simulated diffraction signal is best matched with a measureddiffraction signal. The profile parameters and the one or more processparameters that are used to generate the simulated diffraction signalthat best matches the measured diffraction signal are assumed tocharacterize one or more profile parameters of the structure from whichthe measured diffraction signal was measured and the one or more processparameters used to fabricate the structure. As also mentioned above, theprofile parameters and one or more process parameters can be used toevaluate the fabrication tool and/or fabrication process used tofabricate the structure.

With reference to FIG. 6, an exemplary process 600 is depicted fordetermining one or more profile parameters and/or one or more processparameters for automated process control. In step 602, an opticalmetrology model is created for a structure formed on a semiconductorwafer. The optical metrology model comprises one or more profileparameters, which characterize one or more geometric characteristics ofthe structure, one or more process parameters, which characterize one ormore process conditions for fabricating the structure, and a dispersion,which characterizes optical properties of a material of the structure.

In step 604, a dispersion function is obtained that relates thedispersion to at least one of the one or more process parameters. Instep 606, a simulated diffraction signal is generated using the opticalmetrology model and a value for the at least one of the processparameters and a value for the dispersion. The value for the dispersionis calculated using the value for the at least one of the processparameter and the dispersion function.

In step 608, a measured diffraction signal of the structure is obtainedusing an optical metrology tool. In step 610, the measured diffractionsignal is compared to the simulated diffraction signal. In step 612, oneor more profile parameters of the structure and one or more processparameters are determined based on the comparison in step 610. In step614, the fabrication tool is controlled based on the determined one ormore profile parameters of the structure.

With reference to FIG. 7, an exemplary process 700 is depicted fordetermining one or more profile parameters and one or more processparameters for automated process control using a library. In step 702,an optical metrology model is created for a structure formed on asemiconductor wafer. The optical metrology model comprises one or moreprofile parameters, which characterize one or more geometriccharacteristics of the structure, one or more process parameters, whichcharacterize one or more process conditions for fabricating thestructure, and a dispersion, which characterizes optical properties of amaterial of the structure.

In step 704, a dispersion function is obtained that relates thedispersion to at least one of the one or more process parameters. Instep 706, a simulated diffraction signal library is generated using theoptical metrology model and a value for the at least one of the processparameters and a value for the dispersion. The value for the dispersionis calculated using the value for at least one process parameter and thedispersion function.

In step 708, a measured diffraction signal of the structure is obtainedusing an optical metrology tool. In step 710, a best match to themeasured diffraction signal is obtained from the library. In step 712,one or more profile parameters of the structure and one or more processparameters are determined based on the comparison in step 710. In step714, the fabrication tool is controlled based on the determined one ormore profile parameters of the structure or the determined one or moreprocess parameters.

With reference to FIG. 8, an exemplary process 800 is depicted fordetermining one or more profile parameters and one or more processparameters for automated process control using a trained machinelearning system. In step 802, an optical metrology model is created fora structure formed on a semiconductor wafer. The optical metrology modelcomprises one or more profile parameters, which characterize one or moregeometric characteristics of the structure, one or more processparameters, which characterize one or more process conditions forfabricating the structure, and a dispersion, which characterizes opticalproperties of a material of the structure.

In step 804, a dispersion function is obtained that relates thedispersion to at least one of the one or more process parameters. Instep 806, a set of simulated diffraction signals is generated using theoptical metrology model and a set of values for the at least one of theprocess parameters and a set of values for the dispersion. The value forthe dispersion is calculated using the value for the at least one of theprocess parameter and the dispersion function.

In step 808, a machine learning system is trained to process the set ofsimulated diffraction signals as input and generate the value of the oneor more profile parameters and one or more process parameters as output.In step 810, a measured diffraction signal of the structure is obtainedusing an optical metrology tool. In step 812, the measured diffractionsignal is input into the trained machine learning system. In step 814,one or more profile parameters of the structure and one or more processparameters are determined based on the output of the machine learningsystem. In step 816, the fabrication tool is controlled based on thedetermined one or more profile parameters of the structure or thedetermined one or more process parameters.

The determined one or more process parameters can include depositionconditions, annealing conditions, or etching conditions, and the one ormore fabrication processes can include a deposition process, annealingprocess, or etching process, respectively. The deposition conditions caninclude temperature, gas pressure, and vaporization speed. The etchingconditions can include surface property changes, and etching residualcomponents.

FIG. 9 is an exemplary block diagram of a system for determining andutilizing profile parameters and process parameters for automatedprocess and equipment control. System 900 includes a first fabricationcluster 902 and optical metrology system 904. System 900 also includes asecond fabrication cluster 906. Although the second fabrication cluster906 is depicted in FIG. 9 as being subsequent to first fabricationcluster 902, it should be recognized that second fabrication cluster 906can be located prior to first fabrication cluster 902 in system 900(e.g. and in the manufacturing process flow).

For example, a photolithographic process, such as exposing and/ordeveloping a photoresist layer applied to a wafer, can be performedusing the first fabrication cluster 902. In one exemplary embodiment,optical metrology system 904 includes an optical metrology tool 908 andprocessor 910. Optical metrology tool 908 is configured to measure adiffraction signal off the structure. Processor 910 is configured tocompare the measured diffraction signal against the simulateddiffraction signal. If the measured diffraction signal and the simulateddiffraction signal match within a matching criterion, such as goodnessof fit and/or cost function, one or more values of the profileparameters associated with the simulated diffraction signal aredetermined to be the one or more values of the profile parameters andthe one or more process parameters associated with the measureddiffraction signal are determined to be the one more values of theprocess parameters used to fabricate the structure.

In one exemplary embodiment, optical metrology system 904 can alsoinclude a library 912 with a plurality of simulated diffraction signalsand corresponding one or more profile parameters and one or more processparameters. As described above, the library can be generated in advance;metrology processor 910 can compare a measured diffraction signal offthe structure to the plurality of simulated diffraction signals in thelibrary. When a matching simulated diffraction signal is found, the oneor more values of the profile parameters and process parametersassociated with the matching simulated diffraction signal in the libraryis assumed to be the one or more values of the profile parameters andprocess parameters used in the wafer application to fabricate thestructure.

System 900 also includes a metrology processor 916. In one exemplaryembodiment, processor 910 can transmit the one or more values of the oneor more profile parameters and/or process parameters to metrologyprocessor 916. Metrology processor 916 can then adjust one or moreprocess parameters or equipment settings of first fabrication cluster902 based on the one or more values of the one or more profileparameters and/or process parameters determined using optical metrologysystem 904. Metrology processor 916 can also adjust one or more processparameters or equipment settings of the second fabrication cluster 906based on the one or more values of the one or more profile parametersand/or process parameters determined using optical metrology system 904.As noted above, fabrication cluster 906 can process the wafer before orafter fabrication cluster 902. In another exemplary embodiment,processor 910 is configured to train machine learning system 914 usingthe set of measured diffraction signals as inputs to machine learningsystem 914 and profile parameters and process parameters as the expectedoutputs of machine learning system 914.

Furthermore, a computer readable medium (not shown) such as computermemory, disk, and/or storage may be used to store the instructions andcomputer programs to generate a simulated diffraction signal using adispersion function relating process parameter to dispersion or todetermine one or more profile parameters of a structure and one or moreprocess parameters using an optical metrology model and generatedsimulated diffraction signals using the aforementioned method. Inanother embodiment, computer-executable instructions may be stored in acomputer readable medium to determine one or more profile parameters andprocess parameters using a library comprising simulated diffractionsignals and corresponding profile parameters and process parameters, anda measured diffraction signal. In another embodiment,computer-executable instructions may be stored in a computer readablemedium to train a machine learning system to use a measured diffractionsignal as input and generate one or more profile parameters and processparameters as output. In yet another embodiment, similarcomputer-executable instructions may be stored in a computer readablemedium to control a photolithography cluster or other fabricationcluster using determined one or more profile parameters and processparameters to control a fabrication cluster.

Although exemplary embodiments have been described, variousmodifications can be made without departing from the spirit and/or scopeof the present invention. Therefore, the present invention should not beconstrued as being limited to the specific forms shown in the drawingsand described above.

1. A method of examining a structure formed on a semiconductor wafer using an optical metrology model, the method comprising: a) creating an optical metrology model for the structure, the optical metrology model comprising one or more profile parameters, which characterize one or more geometric characteristics of the structure, one or more process parameters, which characterize one or more process conditions for fabricating the structure, a dispersion, which characterizes optical properties of a material of the structure; b) obtaining a dispersion function that relates the dispersion to at least one of the one or more process parameters; c) generating a simulated diffraction signal using the optical metrology model and a value for the at least one of the process parameters and a value for the dispersion, wherein the value for the dispersion is calculated using the value for the at least one of the process parameter and the dispersion function; d) obtaining a measured diffraction signal of the structure, wherein the measured diffraction signal was measured off the structure; e) comparing the measured diffraction signal to the simulated diffraction signal; and f) determining one or more profile parameters of the structure based on the comparison of the measured diffraction signal to the simulated diffraction signal.
 2. The method of claim 1, wherein e) and f) comprise: (g) determining a matching simulated diffraction signal for the measured diffraction signal; and (h) determining the one or more profile parameters of the structure to correspond to the profile parameters of the optical metrology model used in generating the matching simulated diffraction signal and one or more process parameters associated with the best matched simulated diffraction signal.
 3. The method of claim 1, wherein the dispersion includes a refractive index (n) and an extinction coefficient (k).
 4. The method of claim 1, wherein b) comprises: g) varying values of at least one of the one or more process parameters; h) fabricating a set of wafers, wherein each wafer in the set is fabricated using a different value of the at least one of the one or more process parameters; i) measuring values of the dispersion from the fabricated set of wafers; and j) defining the dispersion function using the measured values of the dispersion and the values of the process parameters used in fabricating the set of wafers.
 5. The method of claim 4, wherein the dispersion function is a polynomial.
 6. The method of claim 1, wherein the one or more process parameters include deposition conditions, annealing conditions, or etching conditions.
 7. The method of claim 6, wherein the deposition conditions may include temperature, gas pressure or vaporization speed, or wherein the etching conditions may include surface property changes or etching residual components.
 8. A method of examining a structure formed on a semiconductor wafer using an optical metrology model, the method comprising: creating an optical metrology model for the structure, the optical metrology model comprising one or more profile parameters, which characterize one or more geometric characteristics of the structure, one or more process parameters, which characterize one or more process conditions for fabricating the structure, a dispersion, which characterizes optical properties of a material of the structure; obtaining a dispersion function that relates the dispersion to at least one of the one or more process parameters; generating a library using the optical metrology model, the library comprising simulated diffraction signals and corresponding values of profile parameters, value for the at least one of the one or more process parameters, and value for the dispersion, wherein the value for the dispersion is calculated using the value for the at least one of the one or more process parameters and the dispersion function; obtaining a measured diffraction signal of the structure, wherein the measured diffraction signal was measured off the structure; obtaining a best match of the measured diffraction signal from the library of simulated diffraction signals; and determining one or more profile parameters of the structure based on the profile parameters of the best matched simulated diffraction signal and one or more process parameters associated with the best matched simulated diffraction signal.
 9. The method of claim 8, wherein the dispersion includes a refractive index (n) and an extinction coefficient (k).
 10. The method of claim 8, wherein the dispersion function is a polynomial.
 11. The method of claim 8, wherein the one or more process parameters include deposition conditions, annealing conditions, or etching conditions.
 12. A method of examining a structure formed on a semiconductor wafer using an optical metrology model, the method comprising: creating an optical metrology model for the structure, the optical metrology model comprising one or more profile parameters, which characterize one or more geometric characteristics of the structure, one or more process parameters, which characterize one or more process conditions for fabricating the structure, a dispersion, which characterizes optical properties of a material of the structure; obtaining a dispersion function that relates the dispersion to at least one of the one or more process parameters; generating a set of training data using the optical metrology model, the training data comprising simulated diffraction signals and corresponding profile parameters, the one or more process parameters, and dispersion, wherein the value for the dispersion is calculated using the value for the at least one of the one or more process parameters and the dispersion function; training a machine learning system using the set of training data, the machine learning system trained to process diffraction signal as input and one or more profile parameters and process parameter as output; and inputting a measured diffraction signal off the structure into the trained machine learning system and generating one or more profile parameters of the structure and one or more process parameters as output.
 13. The method of claim 12, wherein the dispersion includes a refractive index (n) and an extinction coefficient (k).
 14. The method of claim 12, wherein the one or more process parameters include deposition conditions, annealing conditions, or etching conditions.
 15. A system to examine a structure formed on a semiconductor wafer, the system comprising: a photometric device configured to measure a diffraction signal off the structure; and a processing module configured to compare the measured diffraction signal to a simulated diffraction signal, wherein the simulated diffraction signal was generated using a value for at least one process parameter and a value for a dispersion, wherein the value for the dispersion is calculated using the value for the at least one process parameter and a dispersion function that relates the dispersion to the at least one process parameter, and wherein the simulated diffraction signal is generated using an optical metrology model comprising one or more profile parameters, which characterize one or more geometric characteristics of the structure, one or more process parameters, which characterize one or more process conditions for fabricating the structure, and the dispersion, which characterizes optical properties of the materials of the structure.
 16. The system of claim 15, further comprising: a fabrication tool configured to perform a fabrication process on a set of wafers, wherein each wafer in the set is fabricated using a different value of at least one process parameter, wherein values of the dispersion is measured from the set of wafers, and wherein the dispersion function is defined using the measured values of the dispersion and the values of the process parameters used in fabricating the set of wafers.
 17. The system of claim 15 wherein the processing module is further configured to: generate a library comprising simulated diffraction signals and corresponding values of profile parameters, the one or more process parameters, and dispersion, or train a machine learning system to process diffraction signals as input and generate the corresponding one more profile parameters, the one or more process parameters, and dispersion as output. 